Journal of Applied Mathematics and Decision Sciences
Volume 3 (1999), Issue 2, Pages 171-187

On the heat impulse method for deducing sap flow

Ron Gribben

Department of Mathematics, Universiti Brunei Darussalam, China

Copyright © 1999 Ron Gribben. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Speed of sap flow in plants and trees is of interest to botanists and environmentalists because of its connection with the rate of utilisation of nutrients in the soil. An established method uses the transport of heat where an impulsive heat source is introduced along a radial line by a probe in the trunk sapwood. The temperature is monitored, upstream and downstream, and, by solving the heat flow equation in the moving fluid, the sap velocity may be deduced indirectly under some simplifying assumptions which chiefly render the method most useful when applied to trees of relatively large diameter. Transform methods are used to obtain the appropriate threedimensional time-dependent solution in explicit form and values for the resulting sap velocity are compared with the existing two-dimensional theory.